As online shopping channels become ubiquitous, consumers are faced with a vast number of digital purchasing options. To attract more consumers, many e-shops utilize cashback websites (CWs) to provide online rebates. This study examines a dual-channel supply chain, in which the manufacturer sells products through both its own online store and a downstream e-tailer. Both the manufacturer and the e-tailer need to decide whether to offer rebates via CW. We explore the rebate strategy of the two firms as well as its impacts on prices, profit, supply chain, and consumers. Our results show that (i) low-end consumers' valuation plays a significant role on the equilibrium rebate strategy, and interestingly, a scenario where solely the manufacturer provides rebates never emerges in equilibrium. (ii) An intriguing asymmetry emerges: while manufacturer rebates invariably advantage the e-tailer, e-tailer rebates may benefit/hurt the manufacturer. (iii) As the valuation of low-end consumers increases, the equilibrium rebate strategy initially enhances supply chain performance, then diminishes it, and ultimately has no effect. (iv) Low-end consumers benefit from both manufacturer rebates and e-tailer rebates when their valuation is at a medium level. In contrast, high-end consumers incur losses under manufacturer rebates, while e-tailer rebates may either benefit or disadvantage them. In addition, we extend the model to several alternative scenarios, such as simultaneous pricing, temporary rebates, product returns, and coordinated rebates.
ABSTRACT In reward‐based crowdfunding, asymmetric information about product quality can hinder both fundraising success and post‐campaign sales. To mitigate this problem, Belavina (2020) introduces a target‐based deferred payment mechanism, which withholds any funds raised above a prespecified funding target until the creator delivers the promised product to backers. This paper develops a game‐theoretic signaling model to analyze how this mechanism influences strategic behavior in crowdfunding campaigns. The analysis reveals that target‐based deferred payments not only lower the signaling costs for high‐quality creators but also reshape their optimal signaling strategies. Specifically, when the fixed setup cost of producing a high‐quality product is relatively low, high‐quality creators optimally signal their type by offering low reward prices. Conversely, when the fixed setup cost is high, setting a high funding target becomes the dominant separating strategy. The paper further examines alternative formulations of the deferred payment mechanism and offers practical guidance for creators on designing campaigns that credibly signal product quality.
We study a two-stage flexible flow shop scheduling problem aimed at maximizing the total weight of just-in-time jobs, defined as those that complete exactly on their due dates. Two machine configurations are examined: (i) a single common bottleneck machine at stage 1 and parallel dedicated machines at stage 2; (ii) parallel dedicated machines at stage 1 and a single common bottleneck machine at stage 2, where denotes the number of parallel dedicated machines. For the first configuration, we propose a pseudo-polynomial-time dynamic programming algorithm and a fully polynomial-time approximation scheme when is fixed. For the second configuration, we establish that the problem is strongly & Nscr; & Pscr; -hard for arbitrary , even when all jobs have unit weight, and show that it remains ordinarily & Nscr; & Pscr; -hard for under the same condition. We then design a pseudo-polynomial-time algorithm for fixed .
In this paper, we study a dynamic lot sizing problem in which a manufacturer produces a perishable product and supplies it to several customers, each having a different requirement on the product freshness and only accepting inventory stock whose age is not older than a customer-dependent threshold. Both production and inventory holding cost functions are assumed to be concave. The manufacturer makes joint production and inventory allocation decisions to minimize the total cost. We explore structural properties and develop an optimal algorithm for solving the problem in polynomial time. More efficient optimal algorithms are also developed for two important special cases. We conduct computational experiments to demonstrate that the proposed algorithm significantly outperforms the commercial solver CPLEX. Through computational experiments, we also obtain managerial insights into the bottleneck customer, who has the highest freshness requirement.
We consider an integrated production and delivery scheduling (IPDS) problem where each job must be processed on multiple machines in an open shop environment and then delivered in batches to a single customer using a capacitated vehicle. The objective is to minimize the makespan, which captures both production and delivery stages. This model arises in several practical settings, including additive manufacturing and diagnostic laboratories, where tight coordination between production and outbound logistics is critical. Although IPDS has been extensively studied under single-machine, parallel-machine, and flow shop models, the open shop variant has received limited theoretical attention. This paper presents the first constant-factor approximation algorithms with provable worst-case guarantees for the multi-machine open shop IPDS problem. We first introduce a simple two-phase algorithm that achieves a approximation ratio for any fixed number of machines. We then develop a refined approximation algorithm based on a novel framework that combines instance scaling, schedule discretization, configuration enumeration, and LP-based assignment. In the special case of two open shop machines, our result significantly improves upon the best known 2-approximation by tightening the bound to . Importantly, we observe that no algorithm can achieve an approximation ratio below unless , establishing that our algorithm is nearly optimal.
Financial instruments have become an emerging solution to establish sustainable supply chains recently. This paper investigates the effectiveness of a new tool called the sustainability-linked loan (SLL), which contains a sustainability target, a regular interest rate as well as a discounted rate. If borrowers meet the target at the maturity of the loan, they can enjoy an interest discount, otherwise the regular rate is charged. We consider a retailer that procures a single product from a supplier, under which the supplier is capital-constrained and can exert costly effort to raise the product sustainability performance. We study two SLL models: the first one is called the supplier profit-responsibility (SPR) model, where a bank offers the SLL to the supplier, and the bank's objective is to maximize its own profit plus the supplier's effort. Compared with a general loan that contains only an interest rate, the SPR model always induces a higher effort level while weakening the supplier's profit. The second model is called supplier total responsibility (STR) model, under which the bank is totally responsible only to maximize the supplier's effort. We find that the bank's responsibility level (i.e., the weight of effort in the bank's objective function under the SPR model) significantly affects the comparison between the two SLL models. In particular, with a higher responsibility level, while the SPR model induces greater supplier effort, which benefits the retailer, the supplier and the bank obtain lower profits compared to those in the STR model. Furthermore, if the bank's responsibility level is intermediate, the SPR model produces a multi-lose situation: the sustainability level, the profit of the bank and the supply chain are all worse off compared to the STR model. Our results show that when providing the SLL, the bank's preference regarding supply chain sustainability plays a vital role.
To enhance enrollment rates in early-stage dose-finding clinical trials, we propose an information design approach, where the clinical investigator (CI) commits to an information releasing mechanism (IRM) based on the treatment's uncertain efficacy and toxicity to encourage patients to participate in the trial. The optimal IRM has a threshold structure, involving completely revealing/pooling the state (utility) when the realization is in the respective region. We analyze the comparative statics under the optimal IRM. Because general IRMs may be difficult to implement in practice, motivated by response-adaptive clinical trials where information from past patients will help drive decisions for future patients, we consider a practical IRM, where the CI decides on the number of patients to recruit, whose efficacy/toxicity outcomes will be used as information for future patients. For example, the proposed IRM may be the number of patients in the first batch in dose-escalation methods in Phase I, the expansion cohort at the end of Phase I, or the number of patients assigned to the maximum tolerated dose in Phase II. We show that this practical IRM can achieve at most 50% of the value of the optimal abstract IRM. Since patients' risk attitude toward toxicity may be private, we study the impact of belief about it on the optimal IRM and show that the structure of the optimal IRM can be in sharp contrast with that in the public information setting, depending on the distribution of risk attitude toward toxicity. To better understand the impact of the association between efficacy and toxicity on the optimal IRM, we study a bivariate Bernoulli model and show that the optimal IRM has a threshold structure, and the region in which it is a randomized recommendation, when the treatment is ineffective and toxic, shrinks when the association becomes larger.
In this paper, we study an optimization problem for maximizing a generic process's capacity in operations management. Process capacity is defined in this context as the maximum sustainable flow rate. The problem not only considers common features of processes such as collaboration, multitasking, batching, and setups, but also takes account of some features of the processes in which activities are sequentially or parallelly executed and also can be revisited. Unlike previous related analytical studies, we adopt mixed-integer linear programming (MILP) to develop our decision models as well as an exact algorithm for capacity maximization of generic processes considering the aforementioned process features. The benefit of the MILP models lies in their easy extensibility by adding constraints, making them applicable to a broad range of real manufacturing or service operation processes with certain specific features. To shorten the decision time, the exact algorithm also contains some carefully designed cuts and an embedded dynamic programming module with dimensionality reduction and clustering. Managerial insights are obtained using the proposed methodology. For example, as the batch size of each activity increases, the process capacity grows, but as the number of units of each resource increases, the benefit of a greater batch size does not increase. Thus, operations managers should determine an appropriate batch size for each activity, as a larger batch size does not necessarily result in process capacity improvement. The results of this study also suggest that process capacity can be improved through making some, but not all, resources flexible.
This study analytically derives optimal designs for gamma accelerated degradation tests while incorporating inspection time as a design variable under both D- and V-optimality criteria. Under D-optimality, we prove that the optimal design allocates test units exclusively to the lowest and highest stress levels and adopts the longest inspection interval, resulting in only two test groups. In contrast, under V-optimality, although test units are also allocated to the lowest and highest stress levels, the optimal inspection intervals may differ within the same stress level depending on the underlying model parameters, resulting in either two or three test groups. These results can also be applied to the optimal design for gamma-accelerated destructive degradation tests. We further compared our proposed design with conventional V-optimal designs that assume equal inspection intervals across all stress levels. The results demonstrate that conventional V-optimal designs may result in a significant loss of efficiency. Two illustrative examples, an accelerated destructive degradation test and an accelerated degradation test, are provided to demonstrate the practical implementation of the proposed methods and their effectiveness in improving estimation accuracy. Finally, a sensitivity analysis demonstrates that the proposed optimal designs are more robust than the conventional V-optimal design.
In this paper, we study the problem of online learning for a threshold-based inventory control policy in degradable inventory systems with reprocessing capabilities, where the demand is unknown but independent and identically distributed (i.i.d.) across periods. A key feature of our model is that degraded items can be held as inventory rather than being immediately salvaged or reprocessed, providing additional flexibility in operational decisions. Unlike traditional models that assume prior knowledge of the demand distribution, we develop an adaptive learning algorithm to determine the optimal reprocessing and production decisions without such information. Our analysis is motivated by medical supply chains where products like oxygen cylinders degrade over time but can be reprocessed through sterilization and refilling. The model incorporates key operational features including: (1) discrete quality degradation of inventory over periods, (2) the option to hold degraded items in inventory before reprocessing, and (3) the trade-off between production, reprocessing, and inventory holding costs. Through a novel notion of generalized multi-modularity tailored to our state-action structure, we establish the optimality of a state-dependent threshold policy with state-independent threshold parameters, governing both reprocessing and production decisions. When demand is unknown a priori, we propose an online learning algorithm and prove that the algorithm achieves a cumulative regret of . This work contributes to both production-inventory coordination and online learning literature by providing: (1) structural analysis using a generalized multi-modularity framework to characterize the optimal policy in the setting with known demand, (2) the first learning-theoretic framework for reprocessable and degradable inventory systems where degraded items can be strategically held before reprocessing, and (3) theoretical performance guarantees through regret analysis. The methodology applies to various industrial settings where products degrade discretely over time and can be held in degraded states before being reprocessed or salvaged.
We consider a joint production and delivery problem in multi-factory multi-DC (distribution center) multiproduct systems with limited production and delivery capacities over a finite horizon. The objective is to minimize the system's expected total cost. Since the structure of the optimal policy is hard to find, we propose a Lagrangian relaxation heuristic to solve the problem. The proposed heuristic is based on solving a Lagrangian relaxation of the original problem. Although the Lagrangian relaxation problem remains challenging due to the joint production and delivery decisions, we identify a zero-inventory policy that enables further decomposition into independent single-product, single-DC subproblems, each of which can be solved independently. We evaluate the heuristic's performance by deriving a theoretical upper bound on its expected loss. In numerical experiments, we compare the Lagrangian relaxation heuristic with a benchmark myopic heuristic. The results consistently show that the Lagrangian relaxation heuristic achieves a significantly smaller expected relative loss and exhibits greater stability than the myopic heuristic.
Bundle pricing is a widely used strategy in marketing analytics and revenue management, yet most existing heuristics rely on restrictive assumptions about product valuations, such as independence or additivity, and about costs, such as being zero or additivite. We address the mixed bundling problem by proposing a general heuristic algorithm, the pricing-assignment heuristic (PAH), and its extension, E-PAH, which are designed to accommodate heterogeneous customer types and general forms of product interrelatedness, including complementarity and substitutability. The proposed approach alternates between pricing and assignment steps to iteratively improve the seller's profit, and can be initialized from any feasible solution or used as a post-processing tool to enhance existing heuristics. Through extensive numerical experiments, we show that our method consistently outperforms standard benchmarks such as component pricing, pure bundling, and bundle size pricing, achieving on average profit improvements of up to 43% for independent products and up to 53% when products exhibit interdependencies. The algorithm remains effective in the presence of general cost structures, highlighting its flexibility and practical relevance. Overall, the proposed heuristic provides a simple, scalable, and broadly applicable framework for mixed bundling in complex and realistic market environments.
Statistical process control (SPC) methods are commonly employed in various fields to detect distributional changes in sequential processes. Traditional SPC charts are typically developed under the assumption that in-control (IC) process observations are independent and normally distributed with identical parameters. However, when these assumptions are violated, recent research has shown that conventional control charts may become unreliable. To address these limitations, various alternative and flexible control charts have been developed to accommodate autocorrelated observations and nonparametric process distributions. Although existing methods can be reliable and effective when their assumptions hold, they still have some limitations. For instance, methods handling autocorrelated data often rely on parametric time series models or assume equally spaced observations, whereas nonparametric control charts that rely on data ranking or categorization typically suffer from information loss. Furthermore, the optimal performance of many control charts in detecting specific shifts often relies on the accurate specification of their parameters in advance. In this paper, we introduce a novel framework for Phase II online monitoring of univariate processes with irregularly spaced observation times and serial correlation, and the IC distribution cannot be adequately modeled by a parametric form. The method first estimates the IC covariance function for irregularly spaced time series using a local linear kernel smoothing procedure, then sequentially decorrelates the process observations. Next, the decorrelated observations are transformed based on their estimated IC distribution such that the transformed data are approximately standard normal. Finally, an adaptive CUSUM chart is employed to monitor the transformed data. Simulation results indicate that the proposed approach is effective across a variety of scenarios.
Many socially-beneficial services, like dental care, suffer from a dual challenge: Low affordability for citizens and long waiting times due to insufficient provider capacity. We model a government's problem of designing subsidy policies to address this issue. We analyze three financial interventions: Consumer vouchers, which are on the citizen side; and two provider-side subsidies aimed at increasing capacity: Fee-for-service subsidies and downtime rebates. Using a continuous-time Markov chain model, we capture the dynamic interactions between citizens and the service provider in response to these policies. Our findings yield several structural insights into subsidy design. We prove that subsidizing idle service capacity (a form of risk mitigation) always outperforms fee-for-service subsidies (a form of reward enhancement) in terms of cost-effectiveness. However, the choice between citizen-side and provider-side policies depends critically on the primary system bottleneck. To further improve the government's cost efficiency, we propose a mixed-subsidy policy. Although optimizing this policy is intractable, we develop an algorithm to find near-optimal solutions. Numerical experiments demonstrate that a mixed policy combining consumer vouchers with idle-time rebates can offer substantial cost savings compared to the best single-subsidy approach, highlighting the potential efficiency gains of a more integrated subsidy structure.
To accelerate electric vehicle (EV) adoption and overcome the limitations of traditional EV charging-such as long charging time and lack of access to home chargers for urban residents-Battery as a Service (BaaS) has emerged as a promising alternative. Implementing the BaaS model requires investment and operation of battery swapping stations. As both EV manufacturers and battery producers venture into this domain, it raises the question: which party is better positioned to build and operate such infrastructure? We develop a game-theoretical model with one battery supplier and one vehicle manufacturer to compare two BaaS operating models: "manufacturer-operated" model (Model-M) and "supplier-operated" model (Model-S), which differ fundamentally in supply chain structure. In the base model, Model-S induces a larger number of battery swapping stations built. However, Model-M entices more customers to adopt EVs and generates higher profits for the manufacturer. Interestingly, Model-M may also be preferred by the supplier, despite requiring the supplier to cede some decision-making authority. Extending the analysis to a setting with two competing EV manufacturers, we show that the relative efficiency between Model-M and Model-S depends on the degree of downstream competition. Specifically, Model-M tends to be socially optimal in low-competition environments, whereas Model-S gains ground as competition intensifies. Finally, we show that as battery-related costs account for a larger share of total network costs for each additional station built, Model-S becomes the preferred structure for both the manufacturer and supplier over a larger range of parameters. Our paper offers insights for industry leaders and policymakers in determining which party should lead the effort of investing and operating the BaaS model.
Autonomous mobile robots (AMRs) are small, electric, wheeled vehicles that operate at pedestrian speeds. In the last-mile delivery service considered in this study, a fleet of AMRs is deployed across multiple recharging depots within a service area, from which they depart to perform point-to-point deliveries. We consider an operational setting in which AMRs are allowed to travel onboard public transit vehicles, with the objective of extending the service range and reducing energy consumption. To model this problem, we propose two mixed-integer linear programming formulations: an arc-based formulation and a path-based formulation. For the latter, we develop a column generation approach coupled with a four-stage dynamic programming algorithm to efficiently solve the underlying pricing subproblem. This solution approach is further embedded within a rolling horizon framework to address dynamic and large-scale operational settings. A case study conducted in a subregion of Tel Aviv demonstrates the ability of the proposed methodology to handle large-scale instances based on real-world parameters. A sensitivity analysis highlights the effects of request time-window widths, public transit capacity, and AMR battery range on the number of requests that can be served. Finally, the results obtained under the rolling horizon framework confirm the feasibility and practical applicability of the proposed column generation approach.
This paper develops an optimal incentive compensation scheme for a project with a predetermined target but no fixed deadline. A principal sponsors the project and hires an agent to execute it, offering a lump-sum payment that depends only on the project's completion time. The agent exerts a baseline effort level but may increase effort at a personal cost to accelerate progress, balancing the reward from completion against the cost of additional effort. The principal aims to maximize expected payoff, defined as the value of project completion minus the payment to the agent, while also internalizing the cost of delays. Project progress is modeled as a reflected Brownian motion with an agent-controlled drift rate. We solve the associated Bellman equation to characterize the agent's optimal effort and derive the principal's optimal incentive scheme. Extensions include settings in which the agent faces a delay penalty or the principal discounts future rewards. These create additional trade-offs between incentive provision and completion timing. Our numerical experiments further indicate that the principal's payoff is nonmonotonic in the payment level: very small payments produce slow completion, and excessively large payments reduce the net benefit. A finite-horizon extension incorporates project termination at a fixed deadline, which further highlights the role of timing incentives. Throughout, we provide numerical illustrations and managerial insights for designing incentive contracts in target-driven project environments.
Supply chain disruptions can lead to both tactical (i.e., loss of short-term sales during a disruption) and strategic (i.e., loss of long-term market share) consequences. We model the impact of a supply disruption on competing supply chains in which two firms compete for a limited backup supply. We describe strategies for both firms in a two-stage game comprising (i) Preparation, which involves investment prior to the disruption to secure backup supply, and (ii) Response, which involves post-disruption purchasing from the secured backup supply for a component whose availability has been compromised. Firms maximize their long-run profit while simultaneously deciding their preparation and response strategies. We find the equilibrium strategy for firms in the two stages of the game. We describe the conditions under which a firm can use its preparation investment to not only minimize its disruption risks but also capture more market share. We also introduce a Leader-Follower-based game-theoretic model that helps measure each firm's risk exposure by estimating the benefit of preparation. We identify the primary factors that influence the firm's preparation investment and affect customer satisfaction, and show that these depend on the size of the firm and the length of the disruption. This enables us to characterize the appropriate balance between protecting market share and exploiting a disruption to gain market share.
Recent research on social responsibility (SR) communication has focused on upstream supply chains; however, in this study, we analyze how to strategically communicate SR information to consumers in online retailing. We present the optimal SR communication strategies in agency selling and reselling modes and further explore how strategic SR communication strategies affect optimal prices, supply chain members' profits, the platform's SR standard of reselling mode, and the supplier's selling mode selection. The results indicate that both the platform and supplier choose strategically overstated SR communication when the supplier's SR level is moderate, and overstated SR communication is more likely to occur in agency selling with a low marginal selling cost. Interestingly, we find that the overstated SR communication strategy may create a win-win-win situation for the supplier, platform and consumers. Furthermore, SR communication motivates the supplier to choose agency selling. This phenomenon is driven by the profitability of SR overstating, which stems from consumers' additional willingness to pay for SR. The platform can strategically set a proper SR standard for the reselling mode to regulate overstating and encourage the supplier to choose the reselling mode. Counter-intuitively, the optimal SR standard of the reselling mode is the minimum acceptable SR level of socially conscious consumers for products with a high commission rate and a relatively high SR level.
Ensuring timely delivery is crucial with the increasing competition in online meal delivery services. This requires the industry to adopt new technologies and the corresponding operational models, including the use of drones. Concerning the desired features of meal delivery, such as safety and reliability, we propose an operational model that incorporates the usage of drones into the current rider-based delivery model. In our approach, known as drone resupply, drones transport meals from restaurants to riders, and riders then deliver them to customers. We aim to address two key issues when implementing this approach. First, at the operational level, models and algorithms are developed to effectively coordinate rider routing and drone scheduling. These algorithms are tailor-made by leveraging the short routes in the meal delivery industry. Second, at the tactical planning level, we reveal managerial insights to aid meal delivery platforms in making informed decisions regarding the implementation of drone resupply solutions. Particularly, drone resupply proves to be more efficient than rider-only mode across diverse order volumes and service ranges, and remains competitive when the promised delivery time is extended. The effectiveness of drone resupply is closely tied to the fleet configuration of riders and drones, as they have different yet complementary roles in achieving on-time delivery. Additionally, restricting one single order per drone trip does not compromise the effectiveness of drone resupply delivery, but necessitates more demanding drone schedules.
